Calculate magnification and size of biological specimens using millimetres as units.

2.2 Size of Specimens

Learning objectives

• State the relationship between magnification, image size and actual size.
• Calculate any one of the three quantities when the other two are known.
• Convert between millimetres (mm) and micrometres (µm) where required.
• Read an ocular micrometer correctly and understand how it is calibrated.
• Apply the technique safely and recognise the main sources of error.

Key concepts

• Magnification (M) – the factor by which an image is enlarged (or reduced) compared with the real specimen.
• Actual size – the true length or width of the specimen (expressed in mm or µm).
• Image size – the length of the specimen as it appears on the ocular micrometer, screen or drawing (mm).
• Ocular micrometer – a scale fitted in the eyepiece of a microscope; after calibration it is read directly in millimetres.

Fundamental formula

\[ M \;=\; \frac{\text{Image size (mm)}}{\text{Actual size (mm)}} \]

Re‑arranged for the unknown quantity:

1. Actual size = \(\displaystyle\frac{\text{Image size}}{M}\)
2. Image size = \(M \times \text{Actual size}\)
3. Magnification = \(\displaystyle\frac{\text{Image size}}{\text{Actual size}}\)

Unit conversion (mm ↔ µm)

• 1 mm = 1000 µm
• Carry out the calculation in mm, then convert the final answer if the question asks for µm (e.g. 0.020 mm = 20 µm).

Typical instruments and their usual magnifications

Using an ocular micrometer – safety and calibration

• Handle slides with tweezers or a slide holder; never touch the glass with bare fingers.
• Start with the lowest magnification, centre the specimen, then switch to higher power.
• Use the coarse focus gently; never force it at high power.
• Take regular breaks when working at ≥ 400× to avoid eye strain.
• Read the micrometer from directly above to eliminate parallax error.

Calibration of the ocular micrometer

1. Place a stage micrometer (usually 1 mm = 100 divisions) on the stage.
2. Focus the low‑power objective and note how many ocular divisions correspond to 1 mm.
3. Calculate the value of one ocular division: \[ \text{Ocular division (mm)} = \frac{1\ \text{mm}}{\text{Number of ocular divisions covering 1 mm}} \]
4. Record this value; it will be used for all subsequent measurements at that magnification.
5. Repeat the procedure for each objective power you intend to use, because the calibration changes with magnification.

Worked examples

Example 1 – Finding the actual size

A plant cell measures 12 mm on the ocular micrometer when viewed with a 40× total magnification. What is the real length of the cell?

\[ \text{Actual size}= \frac{12\ \text{mm}}{40}=0.30\ \text{mm}=300\ \mu\text{m} \]

Answer given to two significant figures, as required for IGCSE.

Example 2 – Finding the image size

A leaf vein is 2.5 mm long in reality. It is viewed through a 10× hand lens. What length will be recorded on a ruler?

\[ \text{Image size}=10 \times 2.5\ \text{mm}=25\ \text{mm} \]

Example 3 – Finding the magnification

A pollen grain is measured as 5 mm on the ocular micrometer. Its actual size, taken from a textbook, is 0.05 mm. What is the magnification?

\[ M=\frac{5\ \text{mm}}{0.05\ \text{mm}}=100\times \]

Example 4 – Converting units

A bacterial cell is 0.8 µm long. It is observed at 1000× magnification. What is the image size in millimetres?

\[ \text{Image size}=M \times \text{Actual size}=1000 \times 0.0008\ \text{mm}=0.80\ \text{mm} \]

Practice questions

1. A microscope set to 400× shows a bacterial cell as 8 mm on the ocular micrometer. Calculate the actual size of the bacterium (answer in µm).
2. A student uses a 10× hand lens to view a flea. The flea appears 45 mm long on a ruler. What is the real length of the flea?
3. If a pollen grain has an image size of 6 mm at 40×, what would its image size be at 100×?
4. Challenge – A digital photo of a cheek cell is displayed on a computer screen at 2× magnification. The cell measures 30 mm on the screen. What would the same cell measure on the screen if the image were shown at 5×?

Answers

1. Actual size \(= \dfrac{8\ \text{mm}}{400}=0.020\ \text{mm}=20\ \mu\text{m}\).
2. Actual size \(= \dfrac{45\ \text{mm}}{10}=4.5\ \text{mm}\).
3. Actual size \(= \dfrac{6\ \text{mm}}{40}=0.15\ \text{mm}\).
   Image size at 100× \(=100 \times 0.15\ \text{mm}=15\ \text{mm}\).
4. Image size at 5× \(= \dfrac{5}{2}\times 30\ \text{mm}=75\ \text{mm}\).

Common pitfalls & error sources

• Units – Ensure both image and actual sizes are expressed in the same unit before using the formula.
• Formula orientation – Magnification is always *image size ÷ actual size*; swapping the terms gives the reciprocal.
• Significant figures – IGCSE typically requires 2 sf; round only at the final step.
• Parallax when reading the ocular micrometer – View the scale straight on, using the same eye for all readings.
• Calibration error – Always calibrate the ocular micrometer with a stage micrometer for each objective power you use.
• Focus drift – Re‑check the measurement after moving to a new field of view.

Connection to other syllabus topics

• Cell structure (2.1) – distinguishing plant, animal and bacterial cells by size.
• Transport in cells (3.1) – relating diffusion distances to cell dimensions.
• Reproduction (4.2) – measuring gamete and pollen dimensions.

Summary checklist

1. Measure the image size in millimetres (or µm after conversion).
2. Record the total magnification used (or calculate it if required).
3. Apply the appropriate rearranged formula:
   • Actual size = Image size ÷ M
   • Image size = M × Actual size
   • M = Image size ÷ Actual size
4. Convert units where the question demands mm ↔ µm.
5. Round to the required number of significant figures.
6. Check the ocular micrometer calibration, read it without parallax, and follow the safety guidelines.

Suggested diagram